Advertisements
Advertisements
प्रश्न
If y is mean proportional between x and z, prove that xyz (x + y + z)³ = (xy + yz + zx)³.
Advertisements
उत्तर
∵ y is the mean proportional between x and z, then
y2 = xz …(i)
L.H.S. = xyz (x + y + z)3
= xzy (x + y+ z)3
= y2 y(x + y+ z)3 ...[from (i)]
= [y (x + y + z)]3
= [xy + y2 + yz]3 ...[from (i)]
= (xy + xz + yz)3
= (xy + yz + zx)3
= R.H.S.
∵ L.H.S = R.H.S. hence proved.
APPEARS IN
संबंधित प्रश्न
If a/b = c/d prove that each of the given ratio is equal to `sqrt((3a^2 - 10c^2)/(3b^2 - 10d^2))`
If a, b and c are in continued proportion, prove that `(a^2 + ab + b^2)/(b^2 + bc + c^2) = a/c`
If `(28 - x)` is the mean proportional of `(23 - x)`and `(19 - x)` then find the value of x.
If a, b, c, d are in continued proportion, prove that:
(a2 + b2 + c2) (b2 + c2 + d2) = (ab + bc + cd)2.
Find the value of x in the following proportions : 2.5 : 1.5 = x : 3
Find the value of x in each of the following proportions:
55 : 11 : : x : 6
The cost of 4 dozen bananas is Rs 104. How many bananas can be purchased for Rs 6.50?
If `a/c = c/d = c/f` prove that : `bd f[(a + b)/b + (c + d)/d + (c + f)/f]^3` = 27(a + b)(c + d)(e + f)
Write the mean and extreme terms in the following ratios and check whether they are in proportion.
400 gm is to 50 gm and 25 rupees is to 625 rupees
The mean proportion between `3 + 2sqrt(2)` and `3 - 2sqrt(2)` is ______.
